O ( 2 )-symmetry breaking bifurcation : with application to the flow past a sphere in a pipe
O ( 2 )-symmetry breaking bifurcation : with application to the flow past a sphere in a pipe
复制标题
O ( 2 )-对称性破缺分岔：应用于流过管道中球体的流动
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
S. Tavener
中科院分区：
文献类型：
--
作者：
K. Cliffe;A. Spence;S. Tavener
牛顿流体通过管道中心球体的定常轴对称层流首先在定常O（2）对称性破缺分岔点处随流量增加而失去稳定性。利用群论结果，许多作者提出了定位解分支中奇异点的技术，这些解相对于任意群的对称性是不变的。我们提出这些论点的O（2）对称性遇到这里，并讨论其实现O（2）对称的问题。特别是，我们描述了如何分叉点可能首先被检测到，然后准确地定位使用“扩展系统”。此外，它示出了如何决定数字如果分叉分支是亚临界或超临界。采用有限元程序ENTWIFE进行数值求解。这使我们能够计算出一系列球管直径比的破环分叉点。我们还介绍了一个电线沿着的中心线的管道下游的球体，并显示其对临界雷诺数的影响是小的。
The steady, axisymmetric laminar flow of a Newtonian fluid past a centrally-located sphere in a pipe first loses stability with increasing flow rate at a steady, O(2)-symmetry breaking bifurcation point. Using group theoretic results, a number of authors have suggested techniques for locating singularities in branches of solutions which are invariant with respect to the symmetries of an arbitrary group. We present these arguments for the O(2) symmetry encountered here and discuss their implementation for O(2)-symmetric problems. In particular, we describe how a bifurcation point may first be detected and then accurately located using an “extended system”. Also it is shown how to decide numerically if the bifurcating branch is subcritical or super-critical. The numerical solutions were obtained using the finite-element code ENTWIFE. This has enabled us to compute the symmetry-breaking bifurcation point for a range of sphere to pipe diameter ratios. We also introduce a wire along the centreline of the pipe downstream of the sphere, and show its effect on the critical Reynolds number to be small.